Wednesday, November 21, 2007

If I Ran a School... Part 1 Section 1

Mathematics Curriculum.

Establishing a rigourous and effective mathematical curriculum is difficult, to say the least. As stated in the last section, I think students are rushed through calculus. I do see the reason for this: Calculus is the basis of most modern science and engineering techniques; providing calculus at an early age should give them an edge. The problem is that it doesn't.

It is unanimously agreed that Calculus 2 is the hardest calculus course. Why? It isn't because integrating and differentiating trig functions is difficult; it isn't because integration by parts is difficult. So what is it? Trig identities, infinite series, partial fractions. These all have something in common: they are algebra, not calculus. Perhaps if students were given a thorough understanding of algebra before taking calculus, calculus professors could spend their time explaining calculus and proving the theorems, instead of teaching algebra. This way, calculus classes would prove to be the joke they are; hell, you could even get rid of calc 3: it's just calc 1 and 2 with extra variables. If you understand algebra, this is mind-numbingly tedious.

Imagine if history teachers talked about WWII in high school, but didn't mention the Treaty of Versailles, the Weimar republic, or the rise of Totalitarian States until college! It's absurd, isn't it? Well, that's what math instructors do.

I think my tangent is over, let me outline my curriculum. It contains a wide range of useful (to engineering) mathematical topics, as well as some absolutely necessary mathematical knowledge.